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Title: On some laboratory-scale, rotationally-driven viscous flows
Author: Hills, C. P.
Awarding Body: University of Cambridge
Current Institution: University of Cambridge
Date of Award: 2000
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This work considers four flow geometries involving the steady motion of a Newtonian fluid generated, through the action of viscosity, by the rotation of solid boundaries. We are initially concerned with slow-flow, in the low Reynolds number limit, but in most cases some later account is taken of the effects due to fluid inertia. The four problems are all considered in the context of a laboratory scale and our approach simultaneously incorporates the methods of theoretical, numerical and experimental investigation. The first geometry represents an extension of the well-known classical Taylor-Couette flow in the gap between two co-axial, rotating cylinders. We consider the two-dimensional motion of a fluid confined within a rectangular domain and driven by two independently-rotating, disjoint circular boundaries. Our concern is exclusively with the character of the two-dimensional flow in this triply-connected geometry before the onset of any instability. The flow is solved numerically for increasing Reynolds number using a finite-difference scheme over an adaptive Cartesian grid, specially designed to accommodate the circular boundaries. The flow characteristics (streamline topology, vorticity contours and mass transport) are described for a range of geometries, rotation ratios and Reynolds numbers. The topological transitions experienced by the streamline patterns for continuous variation in rotation ratio and geometry are analysed. The two-dimensional theoretical predictions are in qualitative agreement with experimental studies for a range of Reynolds numbers up to the onset of instability to three-dimensional disturbances and the appearance of Taylor cells. It has been previously shown that the existence of a two-dimensional eddy structure near the vertex of a corner depends crucially on the corner angle and arises, in the Stokes approximation for an arbitrary far-field disturbance, as a series of similarity functions with complex eigenvalues. Each of these Moffatt functions itself physically corresponds to a cascade of eddies towards the corner. We consider the particular case when the steady eddy-like flow in the corner is produced by a rotating circular boundary centred at the vertex.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available